Please help me with the correct answer

Answer:

[tex] \dfrac{1}{2} [/tex]

Step-by-step explanation:

we are given a limit

and we want to simplify it

notice that, the numerator is in a sequence of sum of natural number

recall that,

[tex] \rm \displaystyle \: 1 + 2 + 3 + \dots {\dots }+ n = \frac{n(n + 1)}{2} [/tex]

so substitute:

[tex]\displaystyle \lim_{n\to \infty } \frac{ \dfrac{n(n + 1)}{2} }{ {n}^{2} } [/tex]

now recall L'Hôpital's rule

[tex] \displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)} [/tex]

first simplify the complex fraction:

[tex]\displaystyle \lim_{n\to \infty } \frac{n+ 1}{2n} [/tex]

apply L'Hôpital's rule:

[tex]\displaystyle \lim_{ n\to \infty } \frac{ \dfrac{d}{dn} n+ 1}{ \dfrac{d}{dn} 2n} [/tex]

simplify:

[tex] \dfrac{1}{2} [/tex]

and we are done:

Step-by-step explanation:

solution given:

The given expression takes a form[tex] \frac{ \infty }{ \infty } [/tex]

when n=[tex] \infty [/tex]

so,

[tex] \displaystyle \lim_{n\to \infty } \frac{1 + 2 + 3 + \dots {\dots} +n }{ {n}^{2} } [/tex]

[tex] \displaystyle \lim_{n\to \infty }\frac{n(n+1)}{ 2{n}^{2} }[/tex]

[tex] \displaystyle \lim_{n\to \infty }\frac{n+1}{ 2n}[/tex]

[tex] \frac{1}{2} [/tex]

[tex] \displaystyle \lim_{n\to \infty }[1+\frac{1}{ n}][/tex]

=[tex] \frac{1}{2} [/tex](1+[tex] \frac{1}{ \infty }) [/tex]

=[tex] \frac{1}{2} [/tex] is your answer

Answer:

s2Wzwxr tcyvybubububyxrz

Answer:

faces = 7, vertices = 7, edges = 12

Step-by-step explanation:

i took the test just now :D (brainlest always acceptable! :D)

The number of faces, vertices, and edges are 8, 18 and 12.

We are given that;

The figure of hexagonal prism

Now,

A hexagonal prism is a 3D shape with

8 faces, 18 edges, and 12 vertices12.

The faces are 2 hexagons and 6 rectangles.

The figure below shows the faces, edges and vertices of a hexagonal prism.

Therefore, by the prism answer will be 8 faces, 18 edges, and 12 vertices12.

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Step-by-step explanation:

Cos m = 35/37 = 0.94

Cos n = 12/37 = 0.32

Sin m = 12/37 = 0.32

Sin n = 35/37 = 0.94

tan m = 12/35 = 0.34

tan n = 35/12 = 2.91

Answer:

<1 = 33

<2 = 90

<3 = 57

Step-by-step explanation:

<3 = 57 because of alternate interior angles

<2 + <3 + 33 = 180

<2 + 57 + 33 = 180

<2 + 90 = 180

<2 = 90

<1 + <2 + 57 = 180

<1 + 90 + 57 = 180

<1 + 147 = 180

<1 = 33

Answer:

When we know the initial population

, the next thing we need to solve the growth constant

to derive the exponential growth function.

If the problem gives the time it takes for the population to double or the doubling time

τ

. We can find the growth constant by substituting the doubling constant into the equation and solving for t.

This means that the statement is TRUE because the term for initial population cancels out when solving for k and the doubling time is given.

Step-by-step explanation:

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Answer:

19.8,41.8

Step-by-step explanation:

wish you all the best hope you understand.

Answer:

21/4

Step-by-step explanation:

Answer:

The absolute maximum is 4, and the absolute minimum is 2.

Step-by-step explanation:

We are given the function:

[tex]f(x)=x^4-3x^2+4[/tex]

And we want to find the absolute extrema of the function on the interval [-1, 1].

So, we will find the smallest and largest y-value within the interval. First, we can evaluate the function at its endpoints. So:

[tex]f(-1)=(-1)^4-3(-1)^2+4=2[/tex]

And:

[tex]f(1)=(1)^4-3(1)^2+4=2[/tex]

Our endpoints are (-1, 2) and (1, 2).

Recall that extrema only occurs at critical points. Critical points are where the derivative of the function equals 0. So, we can find the derivative of the function:

[tex]\displaystyle f'(x)=\frac{d}{dx}\left[x^4-3x^2+4\right][/tex]

Differentiate:

[tex]f'(x)=4x^3-6x[/tex]

Set the function equal to 0:

[tex]0=4x^3-6x[/tex]

Solve for x. Factor:

[tex]2x(2x^2-3)=0[/tex]

Zero Product Property:

[tex]2x=0\text{ or } 2x^2-3=0[/tex]

Solve for each case. Therefore:

[tex]\displaystyle x=0\text{ or } x=\pm\frac{\sqrt6}{2}[/tex]

The second case is outside of our interval. So we can ignore it.

Evaluate the function at x = 0:

[tex]f(0)=(0)^4-3(0)^2+4=4[/tex]

Therefore, for our function on the interval [-1, 1], the absolute maximum is 4, and the absolute minimum is 2.

Answer:

B. Right angles

Step-by-step explanation:

When perpendicular lines intersect, they create 90° angles (aka right angles)

Answer:

Step-by-step explanation:

450,000=2/3(3.14)r

450,000 times 3/2=2/3(3.14)r times 3/2

675,000=3.14r

675,000/3.14=3.14r/3.14

about 214968.15287=r

So now we know r. We can use it to find the area of the circle

Pi times r squared

3.14 times 214968.15287 squared

area equals about 15573.44815

The area of the hemisphere is 45065.41

The given parameters are:

Shape = Hemisphere

Volume = 450000

The volume is calculated as:

Volume = 2/3pi r^3

This gives

450,000=2/3 * 3.14 * r^3

Solve for r^3

r^3 = 450000 * 3/(2 * 3.14)

This gives

r^3 = 214968.152

Take the cube roots

r = 59.9

The area is then calculated as;

Area = 4pi r^2

This gives

Area = 4 * 3.14 * 59.9^2

Evaluate

Area = 45065.41

Hence, the area of the hemisphere is 45065.41

Read more about areas at:

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Answer:

x = 6

Step-by-step explanation:

10x + 11 + 17x + 7 = 180°

combine like terms:

27x + 18 = 180

subtract 17 from both sides of the equation:

27x = 162

divide both sides by 27:

x = 6

Answer:

y = 0.59x

Step-by-step explanation:

Cost per pound of banana = $0.59

If Number of banana's = x

Total Cost of an item = price per item * number of items

Therefore,

Total cost, y = price per pound of banana * number of bananas

y = 0.59 * x

y = 0.59x

Answer:

Because you first take 75% off of the first price then 25% off the discounted price

Example:

Lets say you have a item that cost $50 and you use a 75% discount card that will make the item $37.5. The you add an additional 25% off which will equal $9.38.

Answer and Step-by-step explanation:

To find the sequence, we must plug in values for n and solve, starting with 0.

f(0) = ⁻13 - 2(0) = ⁻13

f(1) = ⁻13 - 2(1) = ⁻13 - 2 = ⁻15

f(1) = ⁻13 - 2(2) = ⁻13 - 4 = ⁻17

f(1) = ⁻13 - 2(3) = ⁻13 - 6 = ⁻19

When seeing this, we can see that the answer to the questions is A.

#teamtrees #PAW (Plant And Water)

Answer:

Surface area of net = 310 cm²

Step-by-step explanation:

Given:

Dimension of two same rectangle = 11 cm by 9 cm

Dimension of single rectangle = 11 cm by 7 cm

Height of two triangle = 5 Cm

Base of two triangle = 7 Cm

Find;

Surface area of net

Computation:

Surface area of net = Surface area of two same rectangle + Surface area of single rectangle + Surface area of two same triangle

Surface area of net = 2[l x b] + [l x b] + 2[(1/2)(b)(h)]

Surface area of net = 2[11 x 9] + [11 x 7] + 2[(1/2)(7)(5)]

Surface area of net = 198 + 77 + 35

Surface area of net = 310 cm²

hope it helps this to you figthing sheeeeeeeeeeeeeeeeeeeeeeeesh!!!

Answer:

Step-by-step explanation:

These two expressions are definitely not equal.

4 7/9 is a repeating decimal:  4.77777 ...    (use your calculator)

whereqs 4.7 is NOT a repeating decimal.

Answer:

Radius = 2

Step-by-step explanation:

x² + y² - 10x + 8y + 37 = 0

Regroup terms

(x² - 10x) + (y² + 8y) = -37

Complete the square

(x² - 10x + 5²) + (y² + 8y + 4²) = -37 + 5² + 4²

(x² - 5)² + (y² + 4)² = 2²

Center (5,-4)

Answer: 35

Step-by-step explanation:

Answer:

124

Step-by-step explanation:

A triangle is BH/2

6.2 is the height and 5 is the base

one triangle is 15.5 so multiply it by 8 since its an octagon

Answer:

80

Step-by-step explanation:

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Answer:

SU = 15sqrt2

TV = 15sqrt2

SW =(15sqrt2)/2

Step-by-step explanation:

Use the Pythagorean theorem:

X = sqrt(10^2 - 6^2)

X = sqrt(100-36)

X = sqrt(64)

X = 8

Answer:

you can try nine but I am not really sure

Answer:

C

Step-by-step explanation:

At first glance, it seems like all the answers work. But some careful thinking allows us to find the correct answer.

For this question, we will be using the process of elimination.

First, we can eliminate D, because it does not provide any angles on line d, so we cannot prove that line c is parallel to line d.

Second, we can eliminate A. It seems that the 2 angles makes it so that lines c and d must be parallel, however, that is only true if lines a and b are parallel. Since we don't know whether or not lines a and b are parallel, we cannot prove that lines c and d are parallel, so we can eliminate this choice.

Third, we can eliminate B. Like the diagram in A, this diagram can only prove lines c and d are parallel if lines a and b are parallel, and since we don't know whether or not lines a and b are parallel, we cannot prove tat lines c and d are parallel, so we can eliminate this choice.

We are left with C, so the answer must be C.

Of course, just to make sure, we will also check diagram C. Because the 2 angles provided in the diagram are on line a and none are on line b, we do not need line a to be related to line b in any way, as such we can pretend that line b does not exist in this diagram. We can then see that lines c and d must be parallel for this diagram, or else the angles would not work, so C is correct.

Two angles whose sum is 180° are called supplementary angles. The correct option is C.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

When two parallel lines are cut by a transverse. The angles formed on the exterior of the parallel lines are known as the Exterior Angle.

Now, For two lines two be parallel in the given diagram the measure of the angle the exterior angle on the same side of the transverse should be supplementary to each other.

The diagram shows a pair of angle measure that proves lines c and d are parallel in option c. This is because lines c and d are parallel and a is transversal to the two lines. And the measure of the exterior angles formed on the same side of the transversal is supplementary.

Hence, the correct option is C.

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